Question: $ E = \left[\begin{array}{r}-1 \\ 2\end{array}\right]$ $ B = \left[\begin{array}{rr}4 & 1 \\ -1 & 4\end{array}\right]$ Is $ E- B$ defined?
In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ B$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ B$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ B$ Do $ E$ and $ B$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ B$ have the same number of columns? No Yes No No Since $ E$ has different dimensions $(2\times1)$ from $ B$ $(2\times2)$, $ E- B$ is not defined.